When you arrive at (BKK) Bangkok's Suvarnabhumi International Airport and after you have past though immigration and collected your luggage proceed to level 4  which is all departures at the far right end of the departures you will find Domestic departures.

You will be going though the checkin & baggage check again.
When  booking the domestic flight allow at least 2 hours to get though arrivals and passport control .
Suvarnabhumi Airport is very large and can take up to 20mins to walk from the arrivals gate to get to the main terminal.
There's several airlines operating from ( BKK) Suvarnabhumi Airport to (KKC) Khon Kaen Airport.
Thai AirAsia.  Thai Vietjet Air.  Thai Lion Air. Thai Airways ( Including Thai Smile) .

Flight time is approximately 1hour and 5 to 15 minutes.